Hello Naser,

Pearson correlation is a standardized measure of linear association between two sets of scores (standardized, meaning that the result is constrained to be between -1 and +1, as opposed to covariance, which is an unstandardized measure of linear association between two sets of scores).

Spearman correlation is a standardized measure of the linear association between two sets of ranked scores. In fact, it is just a Pearson correlation performed on the ranks of scores (instead of the original values of the scores). Generally, one would select a Spearman correlation if the scores were judged to be of ordinal (able to be ranked) rather than interval (all adjacent scale values represent the same "distance" with respect to that which is measured) strength.

Kendall's correlation (coefficient of concordance, W) is a standardized (between 0 and 1) measure of agreement among multiple features, judges, or some other dimension (could be time/occasion as well). It, as the Spearman, generally would be applied if the data were ordinal in strength (though you could apply it to interval as well).

Good luck with your work.

Good point David

In short:

If you have outliers in your data (i.e. extreme observations), Pearson correlation measures will be distorted and correlation calculations will not be trustworthy.

What to do then? Then you use non-parametric correlation measures: Spearman and Kendall. Kendall is a little bit more sophisticated mathematically than Spearman, but you should expect to get similar results from both non-parametric measures.

David Morse Rolando Gonzales Martinez

Many thanks.

Could you please find the attachment? In the file, I have calculated the correlation matrix using three methods and the last row/column is shown since it would be used to determine the most effective parameters.

Using a non-parametric correlation, it can be concluded that "a_max" and "a_pos" are not influential, whereas using Pearson method, their correlation are somehow equal to a_ave.

Since a_max and a_pos are somehow noisy, can it be concluded that non-parametric correlation is more trustworthy?

Hello again, Naser,

I would need additional information as to the nature of the variables you are correlating, and the number/type of replications (from whence the "avg" and "max" values are derived). Most important, what is it you are trying to determine from this analysis?

Naser Sina well, it really doesn't matter: if you are interested in the correlation of dSOC with a_max and a_pos, both the parametric and non-parametric coefficients suggest that these variables are uncorrelated, since the values of the estimated coefficientes are close to zero. I bet a beer that any null hyphotesis of Ho: rho = 0 will not be rejected at conventional significance levels.

David Morse

Hello David,

Before addressing your comment, I found a useful text on the below link:

http://users.monash.edu/~smarkham/resources/param.htm

In the problem, measurement scale is interval. I've plotted the normal probability curve for each dataset and you can see in the attachment.

I have about 600 samples. My main goal is to estimate dSOC using the most influential parameters using a function estimator neural network. But before that,

I want to justify what are uncorrelated parameters and why should them be neglected.

Rolando Gonzales Martinez

Do you mean null hypothesis for normal distribution?

Naser Sina no, I mean the null:

Ho: rho_xy = 0

i.e. the null hyphotesis that the correlation between x and y is zero.

Rolando Gonzales Martinez Many thanks for sharing your time and knowledge.

Hello, please take a look at this research.

Besides the relation between Matrix; Pearson, Spearman, or Kendall, the research points these statistical coefficients are used for determining the conformity or reliability of experts' evaluations, and the Kendall coefficient with a value greater than or equal to 0.7 was considered as the stopping index for the procedure of the Delphi method.

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